Calculator Usage/Etiquette 

By Chandra Mongroo, Ph.D, Full-time Faculty and Doctoral Lecturer, General Education

This page provides guidance on the appropriate use of calculators, highlighting circumstances where reliance on estimation or algebraic rearrangement may be more advantageous prior to resorting to calculator assistance. By emphasizing the importance of conceptual understanding and procedural fluency, we suggest that calculators should be more of an auxiliary tool rather than primary instrument in problem-solving.

Identifying the appropriate moments to utilize a calculator is crucial for efficiently arriving at solutions in mathematics. While many topics necessitate calculator usage, instances may arise where the problem isn’t immediately conducive to direct input into the calculator. This scenario often occurs when using formulae that require solving for a variable in terms of the others beforehand. Consequently, having a solid grasp of algebraic manipulation is important. Below is a classic example that illustrates this concept, emphasizing the importance of proficiency in algebraic techniques before relying on calculator assistance. 

Example: Consider the following annuity formula from a finance module. 

Suppose we have values for all variables and need to solve for d. The following equation reflects substitution of all known numerical values. 

Here is an extra resource on solving a variable in terms of the others: https://youtu.be/fnuIT7EhAvs 

We are tasked with solving for d. It is recommended to isolate for d. Breaking this down step by step: 

a. Multiply both sides of the equation by (0.06/12):

800000(0.06/12) = d((1 + 0.06/12)³⁰⁽¹²⁾ – 1)

b. Divide both sides by the expression being multiplied by d. 

At this moment, we may use a scientific or graphing calculator to simplify this further. 

Using a calculator you will have two routes: 

1. With proper parentheses placement, input all the values as such: [800000*(.06/12)]/[((1+.06/12)^30(12))-1]. It may look very cumbersome, and it is! This method is not advised at first. 

2. Breaking down the expression step by step working first on simplifying the numerator, then on the denominator abiding by the order of operations. 

numerator = 4,000

denominator = 5.02257521226 ≈ 5.0226

*Note: There will be some rounding error in the calculation. This results from the calculator’s inability to represent the entire string of digits of the number if it is irrational. The less decimal places used in the rounded expression, the more final error that will appear in the solution. 

*Tip: A decent number of decimal places to carry throughout is 4 decimal places (or to the ten thousandths place). 

Resource on rounding errors: https://users.wpi.edu/~goulet/MME523/roundoff.htm